The Girl With The Dragon Tattoo stars Rooney Mara as the traumatised computer hacker and ward of state Lisbeth Salander. Photograph: Merrick Morton/AP

David Fincher turns the film noir white with this steely, stealthy adaptation of The Girl With the Dragon Tattoo. Taking the thriller genre's staple ingredients of murder, sexual sadism and familial corruption, he casts them into the cold, throwing the action across a remote private island, where big pale houses sit against a big pale sky. Outside the snow is flying and the river has frozen. Inside, behind closed doors, it's positively arctic.

Daniel Craig gives a spry, winning performance as Mikael Blomkvist, a disgraced Stockholm journalist who accepts a commission from wealthy industrialist Henrik Vanger (Christopher Plummer), who lives far to the north amid a smattering of brothers and sisters he can hardly bear to speak to. Nominally, Vanger wants Blomkvist to research his memoirs, though what he's really after (or what he says he's after) is the identity of whoever abducted his teenage niece more than 40 years before. "You will be investigating the most detestable people you are ever likely to meet," Vanger announces with relish. "My family."

The film's arrival is the latest instalment in the curious afterlife of the author, Stieg Larsson, who died from a heart attack in 2004. Since then, his posthumously published novel – the first part of his Millennium Trilogy – has sold upwards of 30m copies, as well as spawning a successful Swedish-language film version in 2009.

No doubt many viewers will now be familiar with the yarn's constant twists and turns. Happily, it barely matters: Fincher's expert handling makes this feel as though it's been lifted fresh from the icebox – assuming "fresh" is the right term for a film so steeped in the murk of human cruelty, and so excitedly disgusted by its subject-matter.

Blomkvist's investigation eventually brings him into contact with Lisbeth Salander (Rooney Mara), a turbulent computer hacker and ward of the state, brutalised by the authorities and burning with rage. Salander trusts nobody, possibly not even herself. When Blomkvist tells her, "I want you to help me catch a killer of women," it's the first time she manages to look up and meet his gaze.

If only more high-concept Hollywood thrillers were as supple, muscular and purely gripping. In less experienced hands, this would surely have wound up as lurid, trashy pulp. Yet Fincher plays it straight and keeps it serious. He brings a sense of space and rough edges to a machine-tooled plotline that bounces us remorselessly from clue to clue.

He makes us care about Blomkvist and Salander as they rattle over the island and through the corridors. The route leads them past Nazi skeletons in the closet and arcane references to the Old Testament – all the way down the steps to the basement. Sooner or later, films like this one always wind up underground, in the basement. It's where the secrets are buried, the lights are turned on and the tale turns infernal.

• This article was amended on 23 December 2011. The credit list in the above box included people who worked on the Swedish adaptation of The Girl With the Dragon Tattoo. This has been corrected.